Spring 2017

**Instructor:** Elizabeth Meckes

**Office:** Yost 208

**Phone:** 368-5015

**Email:** ese3 [at] cwru.edu

**Office Hours:** MWF, 11:30 -- 12:30

**Textbook:** We'll be using a draft of the soon-to-be-published *Introduction to Probability* by David
Anderson, Timo Seppäläinen, and Benedik Valkó. It is posted in the Canvas site for this course.

All course information (including the homework assignments!) is posted here; Canvas is used
*only* for grades and a place to post the text book.

Topics | Book chapters | Weeks |
---|---|---|

Random outcomes and the rules of probability Conditional probability and independence |
1,2 | 1-3 |

Random variables | 3 | 4 |

Approximations of the binomial distribution | 4 | 5-6 |

Transformations of random variables Joint distributions |
5,6 | 7-8 |

Sums and symmetry | 7 | 9 |

Expectation and variance | 8 | 10-11 |

Limit theorems | 9 | 12-13 |

Conditional distributions | 10 | 14 |

- Group quizzes 5%
- Homework 15%
- Midterm exams 55%
- Final exam 25%

Forget What You Know About Good Study Habits appeared in the *Times*
in Fall 2010. It offers some advice about studying based on current
pedagogical research.

Teaching and Human Memory, Part 2 from *The Chronicle of Higher
Education* in December 2011. Its intended audience is professors, but
I think it's worth it for students to take a look as well.

Lecture | Quiz | Chapter(s) | Problems | Due date | Reading for next time |
---|---|---|---|---|---|

W 1/18 | 1 | 1.1, 1.2, 1.21 | 1/25 | Sections 1.1, 1.2 | |

F 1/20 | quiz | 1 | 1.5, 1.7, 1.9, 1.10, 1.22 | 1/25 | Sections 1.3, 1.4 |

M 1/23 | quiz | 1 | 1.12, 1.14, 1.15, 1.25 | 1/25 | Section 1.5 |

W 1/25 | quiz | 1 | 1.17, 1.18, 1.19, 1.32, 1.50 | 2/1 | Section 2.1 |

F 1/27 | quiz | 2 | 2.5, 2.6, 2.7, 2.8, 2.28 | 2/1 | Sections 2.2, 2.3 |

M 1/30 | quiz | 2 | 2.9, 2.10, 2.11, 2.34 | 2/1 | Section 2.4 |

W 2/1 | quiz | 2 | 2.13, 2.14, 2.15, 2.17, 2.37 | 2/8 | none |

F 2/3 | quiz | 2 | 2.19, 2.20, 2.22, 2.39 | 2/8 | 2.5 |

M 2/6 | Exam 1 | 2.5 | |||

W 2/8 | quiz | 2 | 2.24, 2.26, 2.59, 2.64 | 2/15 | 3.1 |

F 2/10 | quiz | 3 | 3.2, 3.3, 3.4, 3.26 | 2/15 | 3.2 |

M 2/13 | quiz | 3 | 3.6, 3.7, 3.8, 3.20 | 2/15 | 3.3 |

W 2/15 | quiz | 3 | 3.11, 3.12, 3.13, 3.30 | 2/22 | 3.4, 3.5 |

F 2/17 | quiz | 3 | 3.23, 3.27, 3.35, 3.60 | 2/22 | 4.1 |

M 2/20 | quiz | 3/4 | 3.18, 3.37, 3.39, 4.13, 4.15 | 2/22 | 4.2 |

W 2/22 | quiz | 4 | 4.3, 4.17, 4.20 | 3/1 | 4.3 |

F 2/24 | quiz | 4 | 4.4, 4.5, 4.25 | 3/1 | none |

M 2/27 | Exam 2 | 4.4 | |||

W 3/1 | quiz | 4 | 4.8, 4.28, 4.30, 4.34 | 3/8 | 4.5 |

F 3/3 | quiz | 4 | 4.11, 4.36, 4.45, 4.48 | 3/8 | 4.6, 5.1 (through pg. 165) |

M 3/6 | quiz | 4 | 4.37, 4.40, 4.46, 4.49 | 3/8 | 5.1 |

W 3/8 | quiz | 5 | 5.2, 5.4, 5.5, 5.7, 5.14 | 3/22 | 5.2 |

F 3/10 | quiz | 5 | 5.8, 5.9, 5.15, 5.21, 5.29 | 3/22 | 6.1 |

M 3/20 | quiz | 6 | 6.2, 6.4, 6.18, 6.20 | 3/22 | 6.2 |

W 3/22 | quiz | 6 | 6.5, 6.6, 6.7, 6.22, 6.35 | 3/29 | 6.3 |

F 3/24 | quiz | 6 | 6.8, 6.11, 6.13, 6.25, 6.28 | 3/29 | 6.4 |

M 3/27 | quiz | 6 | 6.15, 6.16, 6.45, 6.49 | 3/29 | 7.1 |

W 3/29 | quiz | 7 | 7.1, 7.3, 7.4, 7.11, 7.12 | 4/5 | none |

F 3/31 | quiz | none | none | ||

M 4/3 | Exam 3 | 7.2 | |||

W 4/5 | quiz | 7 | 7.6, 7.7, 7.8, 7.17, 7.28 | 4/12 | 8.1 |

F 4/7 | quiz | 8 | 8.1, 8.3, 8.5, 8.15, 8.17 | 4/12 | 8.2 |

M 4/10 | quiz | 8 | 8.6, 8.18, 8.27, 8.30 | 4/12 | 8.4 |

W 4/12 | quiz | 8 | 8.9, 8.10, 8.28, 8.34 | 4/19 | 8.4 |

F 4/14 | quiz | 8 | 8.12 (hint: check covariances), 8.42, 8.43, 8.45 | 4/19 | 9.1 |

M 4/17 | quiz | 9 | 9.1, 9.2, 9.3, 9.7 | 4/19 | 9.2, 9.3 |

W 4/19 | quiz | 9 | 9.4, 9.5, 9.8, 9.10, 9.13 | 4/26 | 9.3, 9.4 |

F 4/21 | quiz | 9 | 9.14, 9.16, 9.17, 9.19 | 4/26 | 10.1 |

M 4/24 | quiz | 10 | 10.2, 10.3, 10.12, 10.15 | 4/26 | 10.3 |

W 4/26 | quiz | 10 | 10.14, 10.16, 10.17, 10.24 | uncollected (but good midterm prep!) | none |

- sample space
- event
- probability measure
- probability space
- sampling with replacement
- sampling without replacement
- inclusion/exclusion
- random variable
- distribution of a random variable
- probability mass function
- density
- conditional probability of A given B
- independent events
- independent random variables
- Bernoulli random variable
- binomial distribution
- geometric distribution
- uniform distribution
- Gaussian distribution
- cumulative distribution function
- expected value
- median
- variance
- equality in distribution
- weak law of large numbers
- strong law of large numbers
- Poisson process
- moments
- moment generating function
- equality in distribution
- joint distribution
- joint probability mass function
- joint density
- independent random variables
- jointly continuous random variables
- joint cumulative distribution function
- convolution (discrete case)
- convolution (continuous case)
- Poisson distribution
- Exponential distribution
- exhangeable
- i.i.d.
- sample mean
- sample variance
- covariance
- correlation
- uncorrelated
- positively correlated
- negatively correlated
- Markov's inequality
- Chebychev's inequality
- conditional mass function
- conditional expectation (given an event)
- conditional expectation (given the value of a random variable)
- conditional expectation (given a random variable)

- Poisson distribution
- Exponential distribution
- exhangeable
- i.i.d.
- sample mean
- sample variance
- covariance
- correlation
- uncorrelated
- positively correlated
- negatively correlated
- Markov's inequality
- Chebychev's inequality
- conditional mass function
- conditional expectation (given an event)
- conditional expectation (given the value of a random variable)
- conditional expectation (given a random variable)

- Poisson distribution
- Exponential distribution
- Poisson process
- moments
- moment generating function
- equality in distribution
- joint distribution
- joint probability mass function
- joint density
- independent random variables
- jointly continuous random variables
- joint cumulative distribution function
- convolution (discrete case)
- convolution (continuous case)